Goodness of fit
in [Matlab]
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From: Bo?azici university Tekin on 5 Mar 2010 03:18 Hi ; I have some data. I want to determine the distribution of this data. In order to determine it, I have applied four different probability distribution functions namely, Gaussian( Normal), Rayleigh, Exponential and Weibull by Statistical toolbox. In addition to this, I have obtained each distribution function parameters by Statistical toolbox (such as mean, variance, and other distribution related parameters). When I look at the figures, I can easily see which distribution type is the best one.However, for instances, Weibull and Rayleigh PDF have nearly the similar shape. Therefore, My question is to find the best appriopriate distribution function numerically, not only by looking at the graphs. In other words, I want to determine the best distribution function that fits my data (the best fit for my data). Which one is the best one, Exponential, Weibull, Rayleigh or Normal PDF (probability densty function or distribution function)? I really need your help; Many Thanks; Regards, Gülçin
From: Gulcin Tekin on 5 Mar 2010 10:30 "Gulcin Tekin" <gulcin.tkn(a)gmail.com> wrote in message <hmqenu$4vs$1(a)fred.mathworks.com>... > Hi ; > I have some data. I want to determine the distribution of this data. In order to determine it, I have applied four different probability distribution functions namely, Gaussian( Normal), Rayleigh, Exponential and Weibull by Statistical toolbox. In addition to this, I have obtained each distribution function parameters by Statistical toolbox (such as mean, variance, and other distribution related parameters). When I look at the figures, I can easily see which distribution type is the best one.However, for instances, Weibull and Rayleigh PDF have nearly the similar shape. > > Therefore, My question is to find the best appriopriate distribution function numerically, not only by looking at the graphs. In other words, I want to determine the best distribution function that fits my data (the best fit for my data). Which one is the best one, Exponential, Weibull, Rayleigh or Normal PDF (probability densty function or distribution function)? > > I really need your help; > Many Thanks; > Regards, > Gülçin
From: Frank on 5 Mar 2010 11:22 There's many goodness-of-fit test out there (Chi-squared, KS test, etc.). I personally use the Anderson-Darling gof. Have a look at some of these files... http://www.mathworks.com/matlabcentral/fileexchange/?term=anderson-darling
From: Gulcin Tekin on 5 Mar 2010 13:09 Thanks Frank; But I am new on Matlab. How can I use these files? Can you explian it simply to me:( Thank u very much. Regards, Gülçin Frank <fbleahy(a)yahoo.com> wrote in message <bca7a785-e6cc-4fa2-a1ce-40f0fa019ce9(a)19g2000yqu.googlegroups.com>... > There's many goodness-of-fit test out there (Chi-squared, KS test, > etc.). I personally use the Anderson-Darling gof. Have a look at some > of these files... > http://www.mathworks.com/matlabcentral/fileexchange/?term=anderson-darling
From: Peter Perkins on 5 Mar 2010 13:45
On 3/5/2010 3:18 AM, Bo?azici university Tekin wrote: > Therefore, My question is to find the best appriopriate distribution > function numerically, not only by looking at the graphs. In other words, > I want to determine the best distribution function that fits my data > (the best fit for my data). Which one is the best one, Exponential, > Weibull, Rayleigh or Normal PDF (probability densty function or > distribution function)? While the Statistics Toolbox does have a number of functions to test goodness of fit, this is less of a MATLAB question and more of a statistics question. It might be something to ask on sci.stat.math. Unfortunately, the answer you will get from most statisticians is along the lines of, "what do you mean by "best"?" And they are right, but still, it's not an unreasonable question for you to ask. There are things such as the Kolmogorov-Smirnov test (KSTEST) that are intended to test against a specific know distribution, but that's not what yo are doing. There are things like Lilliefor's test (LILLIETEST) that are intended to test against a family of distributions, but they only exist (to my knowledge) for a few distributions. There's the chi-squared test, which you might try. But In my opinion you were on the right track just by looking at plots. In particular, the DFITTOOL GUI allows you to overlay your data with any number of fitted distributions. CDF plots ar generally the best to use for this. Then you can see how each fitted model captures or fails to capture your data. A simple GOF test isn't going to do that. Hope this helps. |